Question

A small car with mass m and speed 2v and a large car with mass 2m and speed v both travel the same circular section of an unbanked road. If the frictional; force required to keep the small car on the road without skidding is F, then the frictional force required to keep the large car on the road without skidding is
(A) 4F
(B) 2F
(C) F
(D) F/2
(E) F/4

Answer 1

Answer:

(D) F/2

Explanation:

Since the circular section is unbanked, the centripedal acceleration acting on each of the cars is

$a_s = \frac{v_s^2}{r} = \frac{(2v)^2}{r} = \frac{4v^2}{r}$

$a_l = \frac{v_l^2}{r} = \frac{v^2}{r}$

Therefore the centripetal force on each car

$F_s = m_sa_s = \frac{4mv^2}{r}$

$F_l = m_la_l = \frac{2mv^2}{r}$

Since $F_s = 2F_l$ this means the friction force required to keep the large car on the road is only half of the friction force required to keep the small car on road

So (D) F/2 is the correct answer